Trigonometrical calculating and measuring instrument



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No. 537,782.v

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TRIGONOMBTRIGAL GALUULATING AND MEASURING INSTRUMENT.

N0. 537,782. Patented Aprfl, 1895.

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TRIGONOMETRIGAL GALGULATING AND MEASURING INSTRUMENT. No. 537,782.

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A. L. LACOSTE. TRIGUNOMETRIGAL GALOULATING MEASURING INSTRUMENT'.

No. 537,782. f Patented Apnll, 18955.

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A. L.LA`( }OS'IE.I TRIGONOMBTRIGAL GALGULATING AND MEASURING INSTRUMENT.No. 537,782. Patented Apr. 16, 1895.

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Patented Agr. 1 6, 1895.

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i .ADOLPHE L. LACOSTE, OF NA'ICHITOCHES, LOUISIANA.

`TRIGONOMETRICAL CALCULATING AND MEASURING INSTRUMENT.

SPECIFICATION forming part of Letters Patent No. 537,782, dated April16, 1895.

Application tiled January 17,1894. Serial No. 497,136. (No model.)

toches and State of Louisiana, have invented a new and usefulTrigonometrical Calculating 4and Measuring Instrument, of whichthe'following is a full, clear, and exact description.

The invention relates to calculating and measuring instruments, and itsobject is to provide a new instrument which is comparatively simple anddurable in construction, easily manipulated, and more especiallydesigned to enable surveyors and others to readily obtain Without theuse of tables, the sine or cosine corresponding to a, given distance andto a given angle. The said device also forms a mechanical traversetable, giving for any angle and any distance the projections of saiddistance corresponding to said angle, and also forms a mechanical tableof natural sines and cosines.

The invention consists ot' certain parts and details, and combinationsof the same, as will be hereinafter described and then pointed ou in theclaims.

Reference is to be had tothe accompanying drawings, forming a part ofthis specification, in which the same letters .of reference indicate thesame or corresponding parts in all the figures.

Figure l is a plan View of the improved instrument, with grad nationsfrom zero to fortytive degrees. Fig. 2 is a sectional side Veleva-` tionof the same on the line 2-2 of Fig. l. Fig. 3 is a cross section of thesame on the line 3 3 of Fig. l. Fig. 4 is a similar view of the same onthe line L4-4 of Fig. l. Figs. 5 to 25 are diagrammatic viewsillustrating the use ot'- the instrument. Fig. 26 is a plan view of amodification arranged for directly giving sines and cosines for angles'from zero to three hundred and sixty degrees. Fig. 27 is an invertedplan View of the same. Fig. 28

is a sectional .side elevation of the saine on the line 2S-28 of Fig.26. Fig. 29 is a cross section of the same on the line 29-29 of Fig. 26,and Fig. 30 is a similar view of the same on the'line 30-30012' Fig. 26.The improved trigonometrical instrument is provided with a suitable basebeard or other support A, on which are pivoted at B and O the twoparallel arms B and C respectively, pivotally connected with eachotherby a link D so that the two arms B and O, when swinging at their pivots,remain at all times parallel. On the free end of the arm C is arranged aVernier E indicating on a graduation F supported on the base A andarranged on the segment of Va circle, as plainly illustrated in Fig. l.'Ihe graduation Findicates degrees and subdivisions.

The arms B and C are formed with longitudinal slots Bzand O2respectively,A in which are fitted to slide blocks G and H respectively,of which the block G is pivotally connected with the apex of a square ortwo-memberedV arm Lhaving its leg I pivotally connected .with a VernierH', forming part of the slide block H moving in the slot C2 of the armC. The vernier II', indicates on a graduation O3 arranged on the arm Oin alignmentwith the slot C2.

slot A on the top face of the over-hanging` board A2. A block N (seeFig. 4) similar to the block J is fitted to slide in'the slot of the legI of the arm I, the said block N also engaging a transversely extendingslot A3 formed in the over-hanging board A2. The slots A and A3, withthe slide blocks H and J, form guides for keeping the legs I and I2 ofthe square I parallel to their original positions during the movement ofthe arms B and C.

The block N is connected with a Vernier O arranged on top of the boardA2 and formed with a graduation O indicating on a graduai tion Parranged on the upper surface of the the cosines and the graduation Lthe sines.

It is understood that the verniers O and K indicate the respective sineor cpsine for the` 'given vangle and distance.

a l scarse To the above mentioned Verniers can be attached, if,desirable, a clamp and tangent movement screw; also if required areading lens or glass.

In order to conveniently move the several parts, I provide the link Dwith a handle D',

adapted to be taken hold of by the operator so as to impart a swingingmovement to the arms B and C. The handle D is formed with an extensionD2 pivotally connected with an arm Q fulcrumed at Q on the base board Aand arranged parallel to the arm B, as will be readily understood byreference to Figs. l and 8. The length of the extension D2 is equal tothe distance betweenthe pivots B and- Q.

The handle D.' may be provided with clamp and tangent movement screw ifdesired.

On the base board A are arranged the stops A4 and A5 for the arms B andC, so that when the latter rest on the said stops, the Vernier E on theyarm C indicates zero on the graduation F and the two arms B and C areinalignment with each other. When the device is in this position, thesquare or right angle arm I can be readily adjusted forward. andbackward on the arms B and C, whereby the Verniers H and; K are shiftedto indicate atdiifferent points on the graduations C,3 and L, and thedistance may be read either ongraduation Cs or L. When the armi has beenadjusted to the. desired point and the operator shifts the handle Dinward, then the arms-B and C swing attheir pivots and parallel to eachother, whereby the square or right angle arm I is carried along, and thetwo verniers K and O move in their slots A and A3 to indicate thecorresponding sine and cosine for the. angle indicated by the Vernier Eon the. graduation F. The length or distance isv given` by the Vernier Hon thegraduation C3. When the armsB and Care in alignmentwith eachvother, the verniers H and` K should indicate the same Values or numberson gradua-4 tions C2 and L (test of accuracy of instrument).Consequently graduation C3 and its Vernier H could be suppressed anddistance read on graduation L if the instrument is toy be used only as amechanical table of sines and cosines, or as a traverse table. Thegraduation C3 and its Vernier H are however necessary when using theinstrument for solving geometrical problems.

The zero point of the graduation C3 is at the pivot C of the arm C; thezero point of graduation L isin a line extending through the pivots Band Q', and thev zero point of thegraduation P is in a line extendingthrough tion on the over-hanging board`A2 at the given the pivots B'and- C. The graduation F reads from zero to forty-five degrees, upward,and from`- fortyfive degrees to ninety degrees downward, with tivedegrees more or less above the forty-ve degrees, and five degrees moreor less belowk zeroas will be readily nnderstood by reference toy Fig.1.

The connection between the sliding blocks and the respective Verniers isby means of a bolt, as will be readily understood by reference to Figs.2, 3, and 4:, so that the sliding block and Vernier move together, butpermit the part connected therewith to turn whenever movement is givento the several parts constituting the device.

The square or right angle arm I may be arranged in four positions, asindicatedin Figs. 9, lO, 1l and 12, with the result always the same,provided the grad uations of sines and cosines on graduations P and Lare placed in the right position. The square with extended branch, armor leg may also be arranged in following positions, indicated in Figs.I3 to 2O inclusive, with the result always the same provided thegraduations P and L of sines and cosines are placed in the rightposition. The parallel motionl of the arms B and C is secured by meansof the link D, extension D2 and arm Q of Fig. 10r the triangular link DD2. and arm Q' of Fig. 25, or the arms B4 and C4, link D3 and arm Q2 ofFig. 27.

In using the instrument the parts are rst moved' into the position shownin Fig. 5, so that the arms B and C,are in alignment with each other,and then the operator loosens the bolts on the sliding blocks G and H,so as to permit of shifting the square I to the right or to the leftuntil the Vernier H indicates a desi-red distance, say a, on thegraduation C3, the distance reading from zero, correspond- 'ingto thepivot C', to the desired numeral. vAs previously mentioned, the distancea, can

also be read on the graduation L. Now, when the operator pushes on thehandle D', or turns the arm Q2 of Fig. 27, the several parts will moveuntil the Vernier E finally indicates on the graduation F a desiredangle, say e, as plainly shown in Fig. 9.

The Vernier K now indicates on the graduation L a distance n or thecosine corresponding to the distance et `and angle e, provided the anglee is less than 4 the sine corresponding to distance a and angle e,Yprovided angle e is less than forty-five degrees, and the said Vernieralso gives distance m or cosine corresponding to distance ct and anglee, provided angle e is greater than fortyfve degrees. v

It is understood that the same operation is gone through for anyVariation in the distance a and angle e.

Now, if the Vernier C be clamped in posidistance m indicated ongraduation P, and

`the screws on blocks G, H and J, are loosened, then the square I can.be shifted right or left, and it' then the Vernier K is brought to adistance n on the scale L, then the arm C will turn and Vernier E willindicate the angle c; also the Vernier II will slide in the groove C2 ofthe arm C and stop at a distance equal to a at the time the Vernier Estops on IIO IIS

the tangent, as tgr-CO the angle e. Now, let the distance between thepivot C and Vernier Hra; angle e; sine m; and cosine n. When sine m andcosine n are given,`the instrument will at once indicate the distance aand the angle c by operating as explained above. When the sine m andangle e are given the instrument will indicate the cosine n and thedistance a. When sine m and distance a are given, the measuringinstrument will indicate the cosine fn and angle e. When cosine n andangle e are given the sine m and the distance a are indicated by theinstrument, and when cosine n and distance a are given, the sine m andangle c are at once read on the instrument. In other words, any twoelementsof a right angled plane triangle being known or given, theinstrument indicates the other elements. Consequently all cases of rightangled plane triangles can readily be solvedV with the device. 1

The instrument will also indicate the chord of an arc when the angle eand the distance ct are given. As the chord or subtense of an are istwice the sine of one-half the angle given, consequently the side of aninscribed polygon is found when the distance (radius) a andcorresponding angle e are given. The

instrument, by a simple division will also give in s e ,and theco-tangent sine two sides and their included angle are given;

also when two angles and included side are given.

As illustrated in Fig. 6, the instrument is arranged in connection witha sighting device,

which may be a transit or compass said device being so arranged that theline of sight of the compass or opticalaxis or line of collimation oftelescope of transit corresponds exactly with line from pivot C tozero'of vernier E, the center of limb of compass or tran sitcorresponding exactly to center of pivot C and line of sight of compassor optical axis of telescope following all motions of the arm C. Thesight R of the compass or the telescope of the transit is made to alwaysfollow the motion of the arm C, so that the projection of a certain linemaking the angle e with the truenorth line, will be readily read on thescales of the graduationsl and L of sines and cosines as the surveyprogresses.

The instrument above described with coinpass or transit attached andwith the graduation F of only forty-tive degrees will answer the purposeonly for angles less than forty five degrees, it, however, beingunderstood that the instrumentwith graduation from zero to forty-fivedegrees only without compass or transit attached will answer allpurposeslfor office work. It is also understood that any instrumentgiving sines and cosines from zero to forty-iive degrees will also givesines vand cosines for angles from forty-tive degrees to ninety degreesand from zero to three hundred and sixty degrees. In order to avoid thechange of graduation L from scale of cosines to that of sines when theangle is included between forty-tive degrees and ninety degrees, then byhaving the graduation of limb F extended to ninety degrees (see Fig. 6),instead of forty-ve degrees, the graduation L will always remain thescale of cosines, and the same is true as regards the graduation P ofsines with a graduation of zero to ninety degrees for limb F.

In surveying, when using the magnetic needle, the angles read are nevergreater than ninety degrees. Therefore, the instrument with graduationof limb F from Zero to ninety degrees will directly give sines andcosines without change of scales. Theinstrument can also be usedindependent'of the magnetic needle in localities where local attractionis manifested, and this is very desirable 'at times when careful surveysare required. 'i .'lhe graduation Fin this case should then'be usedinstead of the graduation of the compass or transit for reading theangles. Instead of complete compass or transit, compass, sights ortelescope only maybe attached at the pivot C' and made to follow themotion of the arm C and the angles read directly on the graduationF.Such acombination, made in the size of a pocket instrument will be Veryuseful to find directly the distancefrom one point to an inaccessiblepoint, or during war times, for instance, the distance between twoarmies, or the distance to a fortress, dac., to enable artillery to bepointed with accuracy.

By reference to Fig. 8, it will be noticed that the arm Q is parallel toand equal in length to the arm B, and the distance between the pivots Band Q corresponds to the length of the extension D2. -By pushing ordrawing on the handle D', the link D and its extension D2, so that thearms B and C and the arm'Q move in unison and always parallel one to theother, the Verniers K and O always follow. the motion of the square orright angle arm I at the time the arms B and C are swung, as will bereadily understood by reference to Fig. 7, the Vernier Oindicatingincreasing length on the upward movement of the arms B and C, while atthe same time the Vernier K indicates decreasing length, and when thesaid arms B and C swing downward the Vernier K indicates increasinglength and IOO IIO

and C are arranged to make a whole revolution on their pivots B', C withthe squarel of Figs. 26 and 25 following their motions and giving s-inesand cosines on two fixed scales L andP standing at right angles one tothe other.

The square and scales may be arranged in the four positions indicated inFigs. 9, l0, 11, and 12, or it the arm of the square is extended thescales and square can be arranged in eight positions indicated inFigs.13 to 2O inclusive, the result being always the same.

For the instrument showing on its limb F a graduation from zero to threehundred and sixty degrees the same main parts are used as for the onehaving a graduation from zero to forty-five degrees, but the parts aredifferently arranged as indicated in Fig. 25.

The arms B, C, revolvev around their two pivots B and C', and are alwaysparallel in their motion, the arm C having a Vernier reading on thegraduated limb F. The arms B and C, are4 maintained parallel in. theirmotion by the connection ot' link D and triangular link Q, or by linkDand extension D2 ofv Fig. 25, or link D3 and arm Q2 of Fig.. 27, andthe verniers K and` O indicate the sines and cosines.

In orde-r to permit a complete swinging around of the arms B and C, Iextend their pivots through theI base board or support A to the underside` thereof, and secure on the lower ends' of the pivots the arms B4and C4 respectively, pivotally connected with each other by a triangularlink D2, same conn-ection as link D and extension D2 of Fig. 25, alsopivotally connected withl an auxiliary arm Q2 fulcrumed at Q3 on theunder side of the base board, as plainly shown in- Figs. 27 and 30. Thearms B4 and C4, are adapted to indicate on circular graduations F2 F3,respectively formed or secured on the under side of the base board A,and as the said arms stand in perfect alignment with the arms B and Crespectively, they indicate the same degrees as the said arms B and C doon their circular graduations F and F respectively, see Figs. 26 and 27respectively. One only of the four'y graduations F, F', F2 and F2 isnecessary, and it can occupy either of the four positions alluded to. Asshown in Fig. 26, the arm C is provided at each end with a Vernier E.

The improved measuring and calculating instrument with any graduation oflimb F from zero to three hundred and sixty degrees may have attached toit acompass or transit, or a telescope or sight of any kind, to be fixedeither at pivot C or pivot B', and with the line of sight following allmotions of the arms B and C.

Having thus fully described my invention, I claim as new and desire tosecure by Letters Patent- 1. An instrument of the class described,comprising a pivoted moving arm, a square or right angle arm pivotallyconnected with the said arm, and guides for keeping the mem-bers of thesquare parallel to their initial position during vthe ,movement of thesaid pivoted arm, substantiallyvas described.

2. An instrument for the purposedescribed, comprising two pivotedparallel arms, a square whose respective members are pivotallyconnectedto the said arms, slides having movement longitudinally of themembers of the square, and stationary guideways for the slides, saidguideways extending transversely of the members of the square,substantially as described.

3. A measuring instrument ot the class described, comprising two pivotedparallel moving arms, a link for connecting the said arms forsimultaneous movement, and a square or right angle arm held adjustableon the said i parallel arms and moving with the same, substantially asshown and described.

4. A measuring instrument of the class de-y 'right angles 'to eachother, substantially as shown and described.

5. A measuring instrument of the class described', comprising twoLpivoted parallel moving arms, a link for connecting the said arms forsimultaneous movement, a Vernier held on one of the said arms andindicating on a fixed graduation indicating degrees and subdivisions,the` arm carrying the Vernier and also provided with a dfi-stancegraduation, a square or right angle arm held adjustably on the saidparallel arms, a Vernier held on one end of the said square andindicating on the said distance grad nation of the corresponding arm,and two movable verniers controlled from the legs of the said square andindicating on fixed distance graduations arranged at right angles toeach other, substantially as shown and described.

6. A measuring instrument ot the class described, comprising two pivotedparallel moving arms, a link for connecting the said arms forsimultaneous movement, a vernier held on one of the said arms andindicating on a lixed graduation indicating degrees and subdivisions,the arm carrying the Vernier being also provided withadistancegraduation, a square or right angle arm held adj ustably on thesaid parallel arms, a vernierheld on one end of the said squareandindicating on the said distance graduation of the corresponding arm,--two rmovable verniers controlled from the legs of the said square andindicating on xed distance grad nations arranged at right angles to eachother, and intermediate mechanism for connecting the said movableverniers with the legs of the said square, substantially as shown anddescribed.

7. A measuring instrument of the class described, comprising two pivotedparallel moving arms, a link for connecting the said arms IOC forsimultaneous movement, a Vernier held on one of thesaid arms andindicating on a tixed graduation indicating degrees and subdivisions,the arm carrying the Vernier being also provided with a distancegraduation, a square or right angle arm held adjustably on the saidparallel arms, a Vernier held on one end of the said square andindicating on the said distance graduation of the corresponding arm,-two movable Verniers controlled from the legs of the said square andindicating on fixed distance graduations arranged at right angles toeach other, and a handle'held on the said link for actuating the latterand the arms and the i l tance graduation of the corresponding arm,

two movable Verniers controlled from the legs of the said square andindicating on fixed distance graduations arranged at right angles to 3oeach other, and fixed stops for the said arms, tocause the first namedVernier to indicate zero on the degree graduation, substantially asshown and described.

9. An instrument of the class described, 35

comprising a pivoted moving arm, a sighting device secured on the saidarm to move therewith, a square pivotally connected with the said arm,and guides for keeping the members of the square parallel to theirinitial po- 4o sition during the movement of the said pivoted arm,substantially as described.

10. An instrument of the class described, comprising a pivoted movingarm, a two-membered arm pivotally connected to the said mov- 45 ing arm,and guides for keeping the members of the tWo-membered arm parallel totheir initial position during the movement of the said pivoted arm,substantially as described.

` i Witnesses:

A. PLAssAU, B. I-I. HARRISON.

